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Graphs on surfaces and curves over number fields
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Dessins d’enfants and moduli spaces of curves G. B. Shabatab a Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre «Kurchatov Institute» b Russian State University for the Humanities, Moscow |
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Abstract: A very brief overview of the dessins d'enfants theory will be given. Two kinds of its relations with the moduli spaces of curves will be outlined. (1) The Mumford-Penner-Kontsevich-... construction of cell decomposition of (decorated) moduli spaces and its arithmetic version (Mulase-Penkava). (2) The critical filtrations of Hurwitz and moduli spaces, introduced by the speaker, will be provided, some examples given and open questions formulated. |
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